Analysis of nonlinear circuits by using differential Taylor transform

In this paper, an aproximate analytical method called the differential transform method (DTM) is used as a tool to give approximate solutions of nonlinear oscillators with fractional nonlinearites. The differential transformation method is described in a nuthsell. DTM can simply be applied to linear or nonlinear problems and reduces the required computational effort. The proposed scheme is based on the differential transform method (DTM), Laplace transform and Padé approximants. The results to get the differential transformation method (DTM) are applied Padé approximants. The reliability of this method is investigated by comparison with the classical fourth-order Runge-Kutta (RK4) method and Cos-AT and Sine-AT method. Our the presented method showed results to analytical solutions of nonlinear ordinary differential equation. Some plots are gived to shows solutions of nonlinear oscillators with fractional nonlinearites for illustrating the accurately and simplicity of the methods.

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“…Now, the application of the differential transform to Eq. (9), (10) and (12) give the following recurrence relations for 0:…”

Section: Examplementioning

confidence: 99%

“…It has been used to solve efficiently, easily and accurately a large class of nonlinear problems with approximations. These approximations converge rapidly to exact solutions [6][7][8][9][10][11][12][13][14][15][16][17][18][19][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Solution of Nonlinear Oscillators with Fractional Nonlinearities by Using the Modified Differential Transformation Method

Merdan

Gökdoğan

2011

MCA

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“…Accordingly, a new system arises which is now subject to classical boundary conditions, where the boundary conditions at infinity disappeared as a result of the new transformation. The transformed system can be directly solved by the differential transformation method (DTM) [33][34][35][36][37][38][39][40][41][42][43][44][45] without any need to Padé approximants. In this paper, the governing system of ordinary differential equations describing the boundarylayer flow of a nanofluid past a stretching sheet is analyzed through the proposed improved version of the DTM.…”

Section: Introductionmentioning

confidence: 99%

An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid

Ebaid

El-Arabawy

Elazem

2013

International Journal of Differential Equations

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The main feature of the boundary layer flow problems of nanofluids or classical fluids is the inclusion of the boundary conditions at infinity. Such boundary conditions cause difficulties for any of the series methods when applied to solve such a kind of problems. In order to solve these difficulties, the authors usually resort to either Padé approximants or the commercial numerical codes. However, an intensive work is needed to perform the calculations using Padé technique. Due to the importance of the nanofluids flow as a growing field of research and the difficulties caused by using Padé approximants to solve such problems, a suggestion is proposed in this paper to map the semi-infinite domain into a finite one by the help of a transformation. Accordingly, the differential equations governing the fluid flow are transformed into singular differential equations with classical boundary conditions which can be directly solved by using the differential transformation method. The numerical results obtained by using the proposed technique are compared with the available exact solutions, where excellent accuracy is found. The main advantage of the present technique is the complete avoidance of using Padé approximants to treat the infinity boundary conditions.

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“…On the other hand, the differential transform method was used by Zhou [13] to solve linear and nonlinear initial value problems in electric circuit analysis. Analysis of nonlinear circuits by using differential Taylor transform was given by Köksal and Herdem [14]. Using onedimensional differential transform, Abdel-Halim Hassan [15] proposed a method to solve eigenvalue problems.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method

Osmanoglu

Bayram

2013

Abstract and Applied Analysis

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We have considered linear partial differential algebraic equations (LPDAEs) of the form ( , ) + ( , ) + ( , ) = ( , ), which has at least one singular matrix of , ∈ R × . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.

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Analysis of nonlinear circuits by using differential Taylor transform

Cited by 20 publications

References 5 publications

Solution of Nonlinear Oscillators with Fractional Nonlinearities by Using the Modified Differential Transformation Method

Solution of Nonlinear Oscillators with Fractional Nonlinearities by Using the Modified Differential Transformation Method

An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid

A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method

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